An infinite dimensional system is considered and the concept is introduced of the sensitivity operator for the system parameter estimate. The selection of the regularization parameter in the optimization criterion for system identification is discussed. Under an appropriate inequality condition on the regularization parameter, the sensitivity operator can be approximated either by Neumann series partial sums or by an iterative algorithm. In addition, the inequality condition on the regularization parameter provides the possibility not only of ensuring the well-posedness of the system parameter estimation but also of performing an analysis of the sensitivity to observation of the system parameter estimate.